Fixed points and FLRW cosmologies: Flat case

TL;DR

This paper employs phase space analysis to explore fixed points in flat FLRW cosmologies, revealing conditions for avoiding finite-time singularities, the impossibility of finite-time phantom crossing, and the universe's potential end states.

Contribution

It introduces a phase space framework to analyze fixed points in flat FLRW models, including effects of pressure properties and bulk viscosity on cosmic evolution.

Findings

Fixed points prevent finite-time singularities for fluids with finite sound speed.

Phantom crossing cannot occur in finite time under the studied conditions.

The universe's end state is constrained to de Sitter, empty, or recollapsing solutions.

Abstract

We use phase space method to study possible consequences of fixed points in flat FLRW models. One of these consequences is that a fluid with a finite sound speed, or a differentiable pressure, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II and III described in hep-th/0501025. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent $dp/dH$, or a speed of sound is necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to qualitatively describe the entire behavior of a solution in flat FLRW models. We discuss FLRW models with bulk viscosity $\eta \sim \rho^r$, in particular, solutions for $r=1$ and $r=1/4$ cases, which can be expressed in terms of Lambert-W function. The last solution behaves either as a nonsingular phantom fluid or a unified dark fluid. Using causality and stability constraints, we show that the universe must end as a de Sitter space. Relaxing the stability constraint leads to a de Sitter universe, an empty universe, or a turnaround solution that reaches a maximum size, then recollapses.